In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, in a first step, features of the time series need to be extracted. These are numerical quantities that aim to succinctly describe the data and to dampen the influence of noise.

In some applications, these features are also required to satisfy some invariance properties. In this paper, we concentrate on time-warping invariants. We show that these correspond to a certain family of iterated sums of the increments of the time series, known as quasisymmetric functions in the mathematics literature. We present these invariant features in an algebraic framework, and we develop some of their basic properties.

在数据科学中，通常会遇到一个表示一定数量的兴趣量度的时间序列。通常，第一步需要提取时间序列的特征。这些数字量旨在简洁地描述数据并减轻噪声的影响。

在某些应用中，还需要这些功能来满足某些不变性。在本文中，我们集中在时间扭曲不变式上。我们表明，它们对应于时间序列增量的某个迭代总和系列，在数学文献中被称为准对称函数。我们在代数框架中展示了这些不变特征，并开发了它们的一些基本特性。